A piece of wire 100 cm long is cut into two pieces, each to make a square. the area of one square is to be 144cm^2 greater the other.

Question

How should the wire be cut?

Doesn't have to be solved just setup

Answer 1

If you have only 100 cm of wire, then when you cut off x, the two pieces of wire have length x and 100-x.

 

Now, you must form a square with each of these pieces, so one square will have a side length of x/4. Its area will be x^2/16

 

The other square will have a side length of (100 - x)/4. Its area will be [(100 - x)^2]/16

 

One of these squares is larger in area than the other by 144 square centimeters.

 

The equation to solve is as follows:

 

(x^2)/16 + 144 = [(100 - x)^2]/16.

 

The wire must be cut such that one piece is 38.48 cm long. The remaining piece will be 61.52 cm long

The smaller square will measure 9.62 cm on each side and will have an area of 92.5444 square cm.

The larger square will measure 15.38 cm on each side and will have an area of 236.5444 square cm.

The larger square will have an area that is 144 square cm greater than the smaller square.

Answer 2

The two pieces are x and 100 - x

 

The area of one square is x²

The area of the other square is (100 - x)²

 

Area of one square = area of other square + 144

 

x² = (100 - x)² + 144

 

OK?